The above analysis was done with 6 constituent tidal parameters.
I have a home grown spreadsheet that uses a solver plugin that can fit to these tidal patterns.
This is one I did on the same waveform (after digitizing the plot) with 4 major tidal parameters and 4 minor parameters:
The yellow region is training which reached almost a 0.99 correlation coefficient, with the validation region reaching 0.92
This is the complex Fourier spectrum:
I've been wanting to try this for awhile -- to see if the solver setup that I've been using for fitting to ENSO would work for conventional tidal analysis.
Sure enough, if you give it the recommended tidal parameters, the solver will grind away and eventually find the best fitting amplitudes and phases for each parameter.
That's how easy it is to do tsumani detection from buoy data; have about 15 days worth of leading tidal buoy data and continuously update it, comparing it to a model and look for any discrepancies in the sea-level height.